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Proof step 111 from proof junkrefs-put-nopathexplus-equiv (previous step)

refs0 = r1 + refs1, r1 = st[r -- i '] .refval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), junkrefs(str, refs0, st[r -- _type] .type .type, st), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval, ∀ val, sk, r0, st, ty, r, str, refs. # refs < # refs0 → (junkrefs(str, r ' + refs, ty, st) → junkrefs(str, r ' + refs, ty, st[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r, r0, st)) ⊦ r = r0, r = jvmref, sk = _type, refs0 = [], junkrefs(str, r ' + refs0, ty, st[r0 -- sk, val]), path∃+(str, r, r0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 110:
st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), junkrefs(str, st[r -- i '] .refval ' + refs1, st[r -- _type] .type .type, st), ∀ val, sk, r0, st0, ty, r2, str, refs. # refs < # (st[r -- i '] .refval + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r = r0, r = jvmref, sk = _type, path∃+(str, r, r0, st), junkrefs(str, r ' + st[r -- i '] .refval ' + refs1, ty, st[r0 -- sk, val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]